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Answer:
width: 3
Step-by-step explanation:
Given a length l and a width w, we can say that the perimeter is equal to
2 * l + 2 * w. Then, we also know that the perimeter is 27 plus its width, so
2 * l + 2 * w = 27 + w
and the length is 4 times its width, so length = 4 * width = l = 4 * w
We therefore have the two equations
2 * l + 2 * w = 27 + w
l = 4 * w
What we can do is plug 4* w for l in the first equation and solve from there. We thus have
2 * ( 4 * w) + 2 * w = 27 + w
8 * w + 2 * w = 27 + w
10 * w = 27 + w
subtract w from both sides to isolate the w and its coefficient
9 * w = 27
divide both sides by 9 to isolate w
w = 3
l = 4 * w = 12
Therefore, the width is 3 and the length is 12